Semiconductor integrated circuit (IC) fabrication processes involve complex physical and chemical interactions. As the semiconductor fabrication processes become more complex, it is becoming more difficult to predict the outcome of such physical and chemical interactions in the processes. Process models are developed to predict the outcome of these processes. Process models may be a physical model, a black box model or a combination of both. A physical model is based on an understanding of the actual physical processes that occur during a fabrication process and attempts to simulate those processes. Conversely, a black box model is typically a statistical manipulation relying on statistical tools to fit a model to empirical data, but the model itself may have no relation to the actual underlying physical processes.
Physical models tend to exhibit better interpolation and extrapolation results compared to black box models. However, physical models can be computationally complex to implement and may be incapable of accommodating a large number of process parameters that affect the outcome of a fabrication process. On the other hand, black box models can often be extended to accommodate various processing parameters. However, the black box model is only as good as the underlying empirical data, and can suffer from inaccuracy when interpolating or extrapolating from available data points.
Photolithography is the process of transferring patterns of geometric shapes on a mask to a thin layer of photosensitive material (resist) covering the surface of a semiconductor wafer. Photolithography is becoming a more sensitive and critical step in IC fabrication process as feature sizes shrink to ever smaller sizes. Various resolution enhancement techniques have been developed to form smaller features on the IC. One of such resolution enhancement techniques is optical proximity correction (OPC), which uses modified shapes in the mask geometry to account for proximity effects in the exposure process.
Proximity effects can include both an optical effect and a resist effect. The optical effect accounts for optical diffraction caused by patterns on the mask. The optical effect is well understood and analyzed by using Hopkins model, for example. In an actual photolithography process, the proximity effect is greater than anticipated by the optical model. The greater proximity effect is due to non-optical factors that are referred to as the resist component. The resist component includes, among others, acid diffusion, and duration and condition of pre-exposure bake and/or post-exposure bake.
Process models associated with photolithography include constant threshold (CTR) models and variable threshold (VTR) models. The CTR model assumes that any area on a wafer subject to optical energy dose above a constant threshold level is developed. The CTR model is compact, shows good interpolation/extrapolation results, and has low computation requirement. However, the CTR model is incapable of taking various process parameters into account.
On the other hand, most of the VTR model uses statistical tools to fit empirical data to an abstract model not related to the underlying physical processes. Although the VTR model is more advanced than the CTR model and uses statistical techniques to account for variations caused by various process parameters, the VTR model has less connection to the underlying physical processes associated with the photolithography process and, hence, shows limited accuracy when interpolating and extrapolating. Furthermore, the VTR model typically is more computationally intensive compared to the CTR model. The VTR model may also result in double contours instead of a single contour.
Other process models have been developed to account for the resist component of the proximity effect. Such models include, for example, the Mack kinetic development model, the Notch development model, the universal resist dissolution model, the extended Nijboer-Zernike model, acid diffusion models, acid-quencher diffusion models, and full three-dimensional resist development models. However, these models either lack accuracy or require extensive computational resources to simulate the photolithography process.